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Types of Numbers www.mathsrevision.com Level 2 Multiples and LCM Factors and HCF Prime numbers Prime Decomposition 17-Jul-15 Created by Mr. Lafferty Time Left : 0 8 mins 7 6 5 4 3 12 Starter Questions Level 2 31o www.mathsrevision.com Q1. Find all missing angles. 100 92 o 65 Q2. Simplify 135 o 45 o 2 Q3. Find 66 % of 300 3 Q4. I scored 20 out of 25 in Maths and 30 out 40. By working out each percentage score find my best 17-Jul-15 subject. Created by Mr. Lafferty Types of Numbers Multiples www.mathsrevision.com Level 2 Learning Intention Success Criteria 1. We are learning that multiples are simply values in the times tables 1. Remember times tables and use them for multiples. 2. We are learning how to find the Lowest Common Multiple. 2. Apply sets of multiples to identify Lowest Common Multiples 17-Jul-15 Created by Mr. Lafferty Types of Numbers Multiples www.mathsrevision.com Level 2 Example 1 : Find the first seven multiples of 3. M3 = 3, 6 , 9, 12, 15, 18,21 Example 2 : Find the first five multiples of 4. M4 = 4, 8 , 12, 16, 20, ……… 17-Jul-15 Created by Mr. Lafferty Types of Numbers Lowest Common Multiple www.mathsrevision.com Level 2 Lowest Common Multiple Smallest Same Number We need to write out multiples in order to find the Lowest Common Multiple. 17-Jul-15 Created by Mr. Lafferty Types of Numbers Lowest Common Multiple www.mathsrevision.com Level 2 Example : Find the LCM of 3 and 4. M3 = 3, 6 , 9, 12, 15, ……… M4 = 4, 8 , 12, 16, 20, ……… LCM = 12 17-Jul-15 Created by Mr. Lafferty Types of Numbers www.mathsrevision.com Level 2 Now try Exercise 1 Ch5 (page 28) 17-Jul-15 Created by Mr. Lafferty Starter Questions Level 2 www.mathsrevision.com 1. Calculate all the missing angles. 65 o Q2. Find the missing angle. 150 52 o o Q.3 Calculate (a) 17-Jul-15 - 6 + (7 - 8) (b) (-7) x (-19) Created by Mr. Lafferty (c) (-3) x (-8) 4 Types of Numbers Using Factors www.mathsrevision.com Level 2 Learning Intention Success Criteria 1. We are learning that a factor divides into a number with no remainder 1. Identify factors using factor pairs 2. We are learning how to find Highest Common Factors 2. Find HCF for two numbers by comparing factors. 17-Jul-15 Created by Mr. Lafferty Types of Numbers Highest Common Factor www.mathsrevision.com Level 2 Example : Find the HCF of 8 and 12. F8 = 1 and 8 F12 = 1 and 12 2 and 4 2 and 6 3 and 4 HCF = 4 17-Jul-15 Created by Mr. Lafferty Types of Numbers Highest Common Factor www.mathsrevision.com Level 2 Highest Common Factor Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor. 17-Jul-15 Created by Mr. Lafferty Types of Numbers Factors www.mathsrevision.com Level 2 Example : Find the factors of 56. Always divide by 1 and find its pair F56 = 1 and 56 From 2 find other factors and their pairs 2 and 28 4 and 14 7 and 17-Jul-15 Created by Mr. Lafferty 8 www.mathsrevision.com Types of Numbers Now try Exercise 2 Ch5 (page 30) 17-Jul-15 Created by Mr. Lafferty Starter Questions Level 2 www.mathsrevision.com 1. Calculate the area of the following shape. 4 cm 5 cm Q2. Find the missing angle. Q.3 Calculate (a) 17-Jul-15 - 6 +12 - 6 (b) (-7) x (8) Created by Mr. Lafferty (c) (-2) x (-18) 9 Types of Numbers Prime Numbers www.mathsrevision.com Level 2 Learning Intention Success Criteria 1. We are learning what a prime number is. 1. understand the term Prime Number. 2. Find all prime between 1 and 200. 17-Jul-15 Created by Mr. Lafferty Types of Numbers Prime Numbers www.mathsrevision.com Level 2 Definition : A prime number is a number with exactly 2 factors. Example : Is 7 a prime number. Explain? Yes, only two factors 1,7 Example : Is 10 a prime number. Explain? No, more than two factors 1,2,5,10 17-Jul-15 Created by Mr. Lafferty Strike the two’s, strike the three’s the Sieve of Eratosthenes 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100 when the multiples sublime, the numbers that remain are prime! 25 primes Below 100 Use the method of Eratosthenes to find all primes below 200 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 What is the largest prime <200? 46 primes below 200 Range 0 – 1000 1000 – 2000 2000 – 3000 3000 – 4000 4000 - 5000 5000 - 6000 6000 - 7000 7000 – 8000 8000 - 9000 9000 – 10 000 10 000 – 11 000 11 000 – 12 000 Number of Primes 168 135 127 120 119 114 117 107 110 112 106 103 ? Worksheet – www.mathsrevision.com Strike the two’s, strike the three’s the Sieve of Eratosthenes 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100 when the multiples sublime, the numbers that remain are prime! Worksheet – www.mathsrevision.com Strike the two’s, strike the three’s the Sieve of Eratosthenes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 when the multiples sublime, the numbers that remain are prime! Types of Numbers www.mathsrevision.com Level 2 Now try Exercise 3 Ch5 (page 32) 17-Jul-15 Created by Mr. Lafferty Starter Questions Level 2 www.mathsrevision.com 1. Calculate the area of the following shape. 5 cm 8 cm Q2. Find the missing angle. 119 o Q.3 Calculate (a) 17-Jul-15 -16 -12 - 6 (b) (-9) x (5) Created by Mr. Lafferty (c) (-22) x (-11) 2 Types of Numbers Prime Decomposition www.mathsrevision.com Level 2 Learning Intention Success Criteria 1. We are learning what prime decomposition is. 1. Understand the term prime decomposition. 2. Decompose numbers to a product of prime only. 17-Jul-15 Created by Mr. Lafferty Types of Numbers Prime Decomposition www.mathsrevision.com Level 2 A number is either Prime or Composite. (except for 0) If it is composite, like 12, it can always be expressed as a “product of primes” Example : Express 12 as a “product of primes” 12 12 3 All Prime ! 17-Jul-15 3 =3x4 4 2 2 Created by Mr. Lafferty =3x2x2 Types of Numbers Prime Decomposition Level 2 www.mathsrevision.com Example : Express 18 as a “product of primes” 18 18 3 All Prime ! 17-Jul-15 3 =3x6 6 3 2 Created by Mr. Lafferty =3x3x2 Types of Numbers www.mathsrevision.com Level 2 Now try Exercise 4 Ch5 (page 35) 17-Jul-15 Created by Mr. Lafferty